Showing papers on "Parametric oscillator published in 1971"

LINEAR AND NONLINEAR OPTICAL PROPERTIES OF ZnGeP2 AND CdSe

Abstract: The refractive indices of ZnGeP2, point group 42m, have been determined from 0.64 to 12 μ. ZnGeP2 has positive birefringence with reasonable temperature tunability and a band gap in the visible. Its nonlinear optical coefficient d14 for second harmonic generation (SHG) measured relative to d14 of GaAs is 0.83 ± 15%. The birefringence of ZnGeP2 is not large enough to allow phase‐matched SHG, but nondegenerate phase‐matched three‐frequency mixing is possible and the parametric oscillator threshold power is calculated for several situations. A redetermination of the coefficient d31 in CdSe is made and the materials compared. It is concluded that ZnGeP2 may be a most promising material for parametric generation in the 0.8– to 12‐μ region.

Internal optical parametric oscillation

Abstract: The theory of optical parametric oscillation internal to the laser cavity is extended to include the dynamics of the population inversion of the laser medium, thus generalizing it to include all laser-oscillator systems. The equations of motion of the oscillator-laser system are solved by digital computer for the case of a Q -switched Nd:YAG laser with a LiNbO 3 parametric oscillator inside the laser cavity. It is found that this internal optical parametric oscillator operates in a spiking regime, with one or more oscillator pulses per pump pulse. The oscillator pulses inside the nonlinear crystal are often more intense than the laser pulse that would have existed in the absence of parametric oscillation. Oscillator pulse lengths are much shorter than the laser pulse length, with oscillator pulse lengths of typically 5-10 ns compared to laser pulse lengths of 200 ns. The repetition rate of the oscillator pulses is pump-power dependent, with the pulses occurring more frequently as the laser field increases. The theoretical results are compared with experiment, and the analysis is found to provide a good qualitative description of the Q -switched parametric oscillator.

Fluctuations in a parametrically excited subharmonic oscillator

Abstract: The behavior of the classical degenerate parametric oscillator ( \omega_{i} = \omega_{s} ) with small linear dissipation is considered and an expression for the steady-state probability distribution for the subharmonic amplitude is obtained. The treatment is limited to the case 1 \ll Q_{p} \ll Q_{s} where Q p and Q s are the Q factors at respectively the pump and signal frequencies. The behavior is analogous to that of the Brownian motion of a particle in a bistable potential well. This leads to a tractable equation for the relaxation towards the steady-state distribution by thermally activated jumps over the barrier. Near threshold, the behavior is similar to that of a system undergoing a second order phase transition in the mean field approximation. Analogies between first-order phase transitions and transitions in oscillating systems are also pointed out.

Efficient Parametric Mixing in CdSe

Abstract: We have obtained the first phase‐matched nonlinear interaction in CdSe and have observed a 35% conversion efficiency for mixing 10.6 μ with a pump at 1.833 μ to generate a signal at 2.2 μ. The mixing process phase matches at 77° to the optic axis and confirms the predicted phase‐matching angle. The measured nonlinear coefficient value of 2.5 × 10−22 mks agrees with previous results. The mixing experiment shows than an angle‐tuned or pump‐tuned infrared parametric oscillator is possible using CdSe as the nonlinear element.

Instabilities in the doubly resonant parametric oscillator: A theoretical analysis

Abstract: This paper is a theoretical examination of the frequency instabilities of the doubly resonant parametric oscillator. Such instabilities, caused by attempts to resonate simultaneously fields of two frequencies in unstabilized dispersive optical cavities, largely account for the poor performance of early parametric oscillators. The effects of reducing the Q of one of the resonant cavities of the doubly resonant oscillator are treated in detail. An analysis is given that predicts the frequency instabilities resulting from the presence of a slight feedback at the nonresonant mode in a nearly singly resonant oscillator. The analysis shows that the nonresonant mode feedback must be completely eliminated to prevent double-cavity oscillator-frequency instabilities.

Dynamic Stability of Tube Conveying Fluid

Abstract: The parametric resonance of a simply supported tube is studied analytically. By employing Galerkin's method, the equation of motion is reduced to a system of coupled Mathieu-Hill-type equations with multiharmonic coefficients. The stability-instability region boundaries are constructed by the methods of Hsu and Bolotin. The results obtained by Hsu's first approximation show that combination resonance is possible and that the coupling terms do not influence the principal and second instability regions. The higher order approximation is obtained by Bolotin's method which shows that the effect of the coupling terms is to lower, in frequency, the instability regions; they have no effect on the size of the instability regions.

On the Parametric Resonance of a Cylindrical Shell Subjected to a Periodic Axial Load

Abstract: The dynamic stability of thin‐walled circular cylindrical shell is studied for the case of periodic axial load. In computing the internal membrane stress induced by the axial pressures, the cylinder is assumed to act as a longitudinal bar. The internal membrane stress is computed by considering the shell to be a longitudinal rod with axial inertia terms included. Hence, the internal axial coordinate as well as with time and to include the resonances of the cylinder acting as a longitudinal rod. The problem under study is to determine the stability of the flexural motions of the shell oscillating about this inextensional mode. The shell motion is represented by Donnell's equations. A study of the solutions of these equations reveals parametric resonance of the well‐known type and a second parametric resonance which appears to be new. The latter includes the combination resonance between two modes having the same modal pattern, and also between two modes having different modal patterns. In particular, this includes combination resonance between two transverse modes having a different number of axial half waves. This result is believed to be new and is considered the principal result of the study being described. It is only obtained when axial inertia is included in computing the axial membrane stress. It is found that combination resonance does not exist between modes having a different number of circumferential waves. The two modes must have the same number of axial waves. An estimate is given for the width of the unstable regions, and numerical results are presented. The extension to a shell having the effects of rotatory inertia and shear deformation is briefly discussed.

Properties of injection locking in the non-linear oscillator†

Abstract: The detailed behaviours of a non-linear oscillator which is injection-locked by sub-harmonic or harmonic frequency is presented and analysed. The theory, based, on a simple model of the equivalent circuit, can well explain various experimental results. Non-linear oscillator admittance, the combination of both non-linear negative conductance and non-linear susceptance, is found to be a satisfactory model for the injection-locked avalanche diode oscillator.

Detection of movement in confined spaces

Abstract: A radar unit comprises a single microwave launching and receiving antenna, and a microwave oscillator feeding microwave energy to the antenna. A second oscillator is arranged to oscillate at a frequency much lower than that of the microwave energy, and includes an element common to the microwave oscillator. This common element is adapted to respond to load changes on the microwave oscillator, caused by changes in the standing wave pattern of the antenna, by varying at least one oscillation characteristic of the signal provided by the second oscillator. These changes are monitored to provide an indication of the presence and movement of objects in front of the antenna. The microwave oscillator includes a Gunn diode mounted within a resonant cavity and tuned to oscillate at the microwave frequency. An inductance connected in series with the cavity provides a series-tuned circuit of the second oscillator, the cavity providing the common element. The lower frequency oscillations are limited to lie within a predetermined range to improve the sensitivity of the arrangement. This may be done with a feedback circuit. Three such units may be mounted on a common support so as to lie in respective vertical planes at 120* to one another, their combined responses overlapping to provide unbroken coverage in horizontal plane surrounding the common support. The aerials may be shaped to have lobes such that the unbroken coverage extends to a range of some 30 feet from the support.

Extending the Tuning Range of Tunable Oscillators by Upconversion

Abstract: The operation of a doubly resonant LiIO3 parametric oscillator is described. Simultaneous pumping of this oscillator and a LiIO3 upconverter by a single ruby‐laser beam was employed to extend the tuning range of the parametric oscillator down to the 4200–5100‐A range. Up to 10 kW of upconverted power with a 1‐MW ruby‐laser pump was observed; with an intracavity upconverter, a substantial increase in the over‐all efficiency should be achievable.

Simultaneous optical parametric oscillation, second harmonic generation, and difference‐frequency generation

Abstract: We report the observation of simultaneous phase matching of three separate nonlinear optical processes The second harmonic of the signal wavelength of a parametric oscillator was generated and then mixed with the idler wavelength of the oscillator to produce a difference frequency, all in the same nonlinear crystal We have observed 34% average power conversion from the signal to its second harmonic, which is at a shorter wavelength than the pump

Correspondence principle methods applied to a forced harmonic oscillator

Abstract: The correspondence principle for strongly coupled states is used to obtain approximate transition probabilities for a forced harmonic oscillator. For particular forcing potentials, of interest in the vibrational excitation of molecules, the results are shown to be valid even for low order transitions.

Some Consequences of Pump Coherence on Energy Exchange in Nonlinear Optical Processes

Abstract: The finite coherence time of the driving field plays an important role in the rates of energy exchange taking place in nonlinear processes. As a typical example, the problems of the quantum parametric amplifier and frequency converter driven by a fluctuating pump are considered. A closed hierarchy of equations for the moments of the fields is given, which in turn is used for evaluating the average number of photons per mode and the relative variance as functions of time. Significant deviations from the case where the pump field is coherent are found.

Visible CW parametric oscillator using barium sodium niobate

Abstract: Visible thermal tuning CW parametric oscillator using barium sodium niobate as nonlinear material

Simultaneous Optical Parametric Oscillation and Second‐Harmonic Generation

Abstract: The simultaneous occurrence of optical parametric oscillation and second‐harmonic generation (SHG) of the oscillator signal or idler is studied. These processes, which occur in a single crystal, generate a new output which, depending upon whether the signal or idler is involved, can lie above or below the pump wavelength. This effect is of interest because (1) it provides a technique for generating a tunable output in the vicinity of the oscillator pump and (2) in normal oscillator operation, it is undesirable since it acts as a loss mechanism for the signal. We show that the simultaneous occurrence of oscillation and SHG is a phenomenon which can occur in a number of parametric oscillators. Techniques are given for predicting and studying this process for any nonlinear material. Methods of tuning the generated second harmonic (SH) are also considered. Experiments were performed on an oscillator/doubler consisting of a single lithium niobate crystal pumped by a repetitively Q‐switched 1.06‐μ laser. More t...

Adiabatic Invariance in Simple Harmonic Motion

Abstract: We show, in an elementary but apparently new way, that the ratio of the energy to the frequency of a simple harmonic oscillator is an adiabatic invariant. The adiabatic invariance is a consequence of the conservation of angular momentum in the two-dimensional system, of which the one-dimensional harmonic oscillator is the projection. We also briefly discuss the connection between the quantization of angular momentum and the quantization of the oscillator's energy.

Voltage controlled oscillator multiplier

Abstract: A voltage controlled oscillator and varactor multiplier circuit having a varactor network coupling the output of an oscillator through a band pass filter to an output in which a single varactor produces frequencies tuned by varying the bias thereon and produces frequency multiplication.

A parametric amplifier for 46 GHz

Abstract: A degenerate parametric amplifier for 46 GHz is described. It uses a Schottky barrier varactor packaged in a modified Sharpless wafer. The novel amplifier mount construction, which uses no tuning screws, yields predictable and reproducible results. In good agreement with theory, 14-mW pump power was required and a noise temperature of less than 400°K was measured.

Horizontal oscillator disabling circuit control apparatus

Abstract: Concurrently filed United States Patent application Ser. No. 144,457, entitled ''''HORIZONTAL OSCILLATOR DISABLING CIRCUIT'''' describes a means of shifting the frequency of the horizontal oscillator of a television receiver in the presence of high voltage increases which could cause X-radiation problems. As therein described, a negative direct voltage indicative of the developed ultor potential for its cathode-ray tube is combined with a relatively stable positive direct voltage to change the bias on a control transistor and the effective resistance in the time constant network determining the oscillator frequency. The present invention provides a further positive direct voltage to the transistor from the brightness control network of the receiver, so as to control the point at which the oscillator goes off frequency as a function of picture tube beam current. Such further voltage will be seen to reduce the criticality in determining the point at which the frequency shifting is to occur and the point at which the reproduced picture becomes unviewable.

Improvements in the theory and design of RC oscillators

Abstract: The general oscillator theory pertinent to frequency stability is presented, and the superiority of the bridge oscillator is demonstrated. The tables provided show the similarity between the transfer functions, and certain other network functions, of the commonly used RC oscillator networks. These networks are optimized for use in frequency stable oscillators, and some very simple constraints are found for the parallel- T network. Contrary to the ideas of previous authors the best network for an RC oscillator cannot be established theoretically. Instead, it is shown that the seven networks given fall into only three groups. Together these groups provide a continuous range of the two major properties required for good frequency stability. These properties must be chosen empirically to match the amplifier used in a particular oscillator.

Collisional Excitation of Vibrational Energy of an Initially Excited Harmonic Oscillator

Abstract: An analytical formula for the phase‐averaged vibrational energy transfer to an initially excited harmonic oscillator is presented.

Temperature compensated tuner and oscillator

Abstract: An oscillator the tuned element of which comprises a resonant cavity, may vary in frequency as the temperature thereof varies. An oscillator of the cavity type is disclosed in which means are provided to reduce the variation of oscillator frequency with temperature change comprising a dielectric rod and means to move the rod more or less into the cavity comprising a pre-stressed metallic element which is held in a bowed shape by another metallic element, the temperature co-efficients of expansion of the two metallic elements being different.

Signal controlled wide range relaxation oscillator apparatus

Abstract: A wide range oscillator which can operate over approximately a 104 frequency range. The oscillator uses a current controlled ramp generator which varies the charging rate of an integrating capacitor. The wide range of charging current plus a low discharge time of the integrating capacitor combines to enable a very wide frequency range oscillator.

On a Unified Theory of Twocentre Harmonic Oscillator Integrals. I. The Onedimensional Oscillator

Abstract: Abstract Twocentre harmonic oscillator overlap integrals, arbitrary transition integrals and collision energy etchange integrals for equal and different frequencies of the oscillators are contained in a generalized Franck-Condon-integral which is solved by operator methods in the second quantization representation.